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STRENGTH PROPERTIES
OF MACHINE cameo "LUMBER

. Thesis for the Dogma .of M. S

MICHIGAN STATE UNIVERSITY +_
Gerard JQ Teit.sma.,  

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Michigan "“3326 I
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ABSTRACT
STRENGTH PROPERTIES OF
MACHINE GRADED LUMBER

by Gerard J. Teitsma

One hundred-fifty nominal 2" by 8" Douglas fir boards
were tested to determine the strength properties of machine
graded lumber. The sample was composed of fifty boards each
of three machine grades; 1500f, 2100f, and 2h00f.

Each board was graded visually and subsequently subjected
to major and minor tests. In the major tests, the boards were
tested for modulus of elasticity and modulus of rupture using
an approximately uniform load over a simply supported ten foot
span. The modulus of elasticity was calculated for the con-
dition of load applied to each of the four sides. The modulus
of rupture was determined with members loaded as a joist. In
the minor tests, small samples from each board were used to
determine Specific gravity, moisture content, and clear wood
modulus of elasticity and rupture.

Bar charts were drawn to show the relationship between
the modulus of rupture and each of the EMSR*and visual grades.
Points were also plotted to show the modulus of rupture (MOB),
as a function of plank modulus of elasticity (MOE), Joist MOE,
stiffness, slope of grain, Specific gravity, and clear wood
modulus of rupture. Additional graphs were drawn to show other
relationships between major and minor test variables.

Test results indicated that neither EMSR or visual stress

grading systems were reliable in predicting the ultimate strength

 

*Electro Mechanical Stress Grade

Abstract
Gerard J. Teitsma
Page 2
of the board. Graphs plotted to show joist modulus of rupture
as a function of plank modulus of elasticity resulted in a
correlation coefficient of approximately 0.70. Calculating
MOE as a joist did not result in a better correlation with
joist MOB.

Specific gravity, slope of grain, and clear wood MOB
had little influence on board MOB indicating that the breaking
strength of the boards was due mainly to the defects in the

boards.

STRENGTH PROPERTIES OF
MACHINE GRADED LUMBER

By

Gerard J. Teitsma

A THESIS

Submitted to
Michigan State University
in partial fulfillment of the requirements
for the degree of

MASTER OF SCIENCE

Forest Products Department

1966

ii \0

TABLE OF CONTENTS

ACKNOWLEDGMENTS . . . . . . . .
LIST OF TABLES .

LIST OF ILLUSTRATIONS .
INTRODUCTION . . . . .
LITERATURE REVIEW . . . .
PURPOSE . . . . . . .

TESTING PROCEDURE .

Preparation and Description of

Large Scale Test Procedure .

Small Scale Test Procedure

TEST RESULTS . . . . . . . . .

Modulus of Rupture of Boards

EMSR and Visual Grades .
Modulus of Elasticity .
Stiffness Properties . .
Slope of Grain . . . . .
Specific Gravity . .

Samples

Clear Wood Modulus of Elasticity

Clear Wood Modulus of Rupture

Moisture Content . . . .
DISCUSSION OF RESULTS . . . . .
CONCLUSIONS .

APPENDIX I - Statistical Methods Used .

APPENDIX II - Equations . .-1 .
APPENDIX III - Data . . . .
LITERATURE CITED . . . . . .

O O O O O O O

Page
ii
iii

iv

10

10
ll

19
23
23
26
27
27
28

28
29

52
58
59
62
66

69

ACKNOWLEDGMENTS

The writer wishes to express his sincere thanks to
Professor Byron M. Radcliffe for his help in formulating
the problem and for his valuable advice concerning the
research and preparation of this thesis. He would also
like to express appreciation for the suggestions and
assistance of Dr. Alan Sliker.

In addition, the writer is indebted to all of the
other faculty members of the Forest Products Department
and to his fellow graduate students for their encourage-

ment and assistance.

11

LIST OF TABLES

Table Page
1. Statistics Used to Compare Data . . . . . . 30
2 . Appendix III " Data 0 o o o o c o o o o o o 67

111

Figure
1.

LIST OF ILLUSTRATIONS

Method of Measuring Boards to Determine
Moment of Inertia . .

O C 0 0 O I O 0

Large Scale Test Apparatus . . . . . . .

Testing Load Deflection Properties as a
Joist and as a Plank

O 0 O 0 O O O O

Direction of Load Application . . . . .

Testing for Modulus of Rupture . . . .

Comparison Between Visual and EMSB Grades

EMSB Grade vs. MOB

O O 0

Visual Grade vs. MOB . .

Joist MOB vs. Plank MOE

Joist MOB vs. Joist MOE

MOB vs. MOE Within
MOB vs. MOE Within
MOB vs. MOE Within
MOB vs. MOE Within
MOB vs. MOE Within
MOB vs. MOE Within

MOB vs. MOE Within

1500f
2100f
2400f
1200f
1500f
1900f
2050f

EMSB Grade . .
EMSB Grade . .
EMSB Grade . .
Visual Grade .
Visual Grade
Visual Grade

Visual Grade .

Joist MOB vs. Stiffness LEI) . . . . . .

Joist MOB vs. Slope of Grain . . . . . .

Joist MOB vs. Specific Gravity . . . . .

Plank MOE vs. Joist MOE

Plank MOE vs. Specific Gravity . . . . .

iv

Page

13
14

16
18
21
2a
31
32
33
34
35
36
37
38
39
no
41
112
1+3
an
45
as

Figure Page
23. Plank MOE vs. Clear Wood MOE . . . . . . . . . #7
24. Joist MOB vs. Clear Wood MOB . . . . . . . . . 48
25. Clear Wood MOB vs. Clear MOE . . . . . . . . . 49
26. Clear Wood MOB vs. Specific Gravity . . . . . 50
27. Clear Wood MOE vs. Specific Gravity . . . . . 51

28. Major Test Shear and Bending Moment
Diagrams . . . . . . . . . . . . . . . . . 64

INTRODUCTION

The mechanical properties of clear wood within a
species vary because of generic and environmental factors
which cannot be controlled by the forester or lumber man-
ufacturer. Due to natural and manufacturing defects in
commercial lumber, this variability is compounded. In
order to estimate safe design values for mechanical
properties for structural design purposes, systems for
visually examining a board and predicting its strength
have been in use for many years.

The upper limit criteria for the visual stress
grades of joists and planks are the basic stress values
established for clear sound wood within a species. The
basic stresses are established by applying standard reduc-
tion factors to the average strength and stiffness properties
as determined from large numbers of ASTM tests of small,
clear specimens. The ASTM beam specimens are tested in a
green condition (above the fiber saturation point) which
eliminates variability due to moisture content. The moduli
of rupture and elasticity are least for the green condition
as regards the effect of moisture content. The average MOB
value is multiplied by reduction factors as follows; 3/4
for sample variation, 9/16 for duration of load, 3/5 for a

2
factor of safety and 9/10 to account for unknown service
condition. Thus the basic MOB*value is about 22.8 percent
of the average breaking strength of clear green ASTM beam
specimens. The basic value for E, however, is about the
same as the average found in tests reduced slightly for a
depth factor value of about 9/10.

It is important to note that the application of such
reduction factors results in a 95 percent lower confidence
limit for each variable independently. By multiplying all
such reduction factors together, it is assumed that the lower
limit for every variable applies to every joist or plank in
actual use. Thus, basic stress values for MOB are unreal-
istically low.

The basic strength values constitute the upper limit
for arriving at the visual grades. According to the number,
size, and location of strength reducing characteristics such
as knots, slope of grain, wane, and seasoning defects, an 'f'
grade (allowable flexural strength in psi) is assigned in
accordance with standard published grading rules. There are
several 'f' grades for every structural species in the joist
and plank classification.

Even though the visual grading techniques have been
shown to be inaccurate and overly pessimistic, Visual grading
has remained the standard method. This has been due primarily
to an abundance of low cost lumber and lack of a better grading
method. However, two factors have become increasingly important
which require some better system of lumber grading be developed;

(1) increase in cost of lumber compared to competitive structural

 

*Basic stress for extreme fiber in bending.

3
materials and (2) improved method of using other materials in
light construction as a result of research and development by
manufacturers and more wide spread increased mechanization of
building techniques.

The most effective means of grading suggested has been
some form of non-destructive evaluation of mechanical behavior
of each board individually. Modulus of elasticity is a mechan-
ical property which can be determined without destroying a
piece of material. The problem then resolves itself into
finding reliable empirical parameters to predict the ultimate
strength values as functions of MOE which could be reduced by
reasonable realistic safety factors to give allowable design
stresses.

In the past five years, two stress grading machines
have been developed and are commercially available. The
designs of these machines are based upon exhaustive test
results for determining a formula relating MOB to MOE. The
equation which is used has reductions included, allowing for
duration of load, depth factor, and safety factor. Both
machines are calibrated so that the boards will have MOB
values of 2.1 or greater times the working stress for the
grade for 95 percent of the pieces produced. The 2.1 factor
is a combination of load duration factor and other factors
of the type traditionally applied.

Potlach Forest Industries developed one of these
machines called the Industrial Sciences CLT-l (Continuous
Lumber Tester) in cooperation with Industrial Sciences of

Portland, Oregon. The other stress grading machine was

LI,
pioneered by the Western Pine Association and is being
manufactured by the Tri-State Machinery Company of Dallas,
Texas.

The four ton CLT-l costs approximately $45,000. It
is a highly sophisticated machine incorporating computer
components and a memory storage system. At the infeed side
of the machine, a roller system deflects the pieces 5/16 inch.
The pieces are deflected 5/16 inch again in the opposite
direction on the outfeed side of the machine, providing the
average values of load required. The force required to deflect
the piece 5/16 inch is measured by two transducers. The output
of each transducer is stored into a capacitor storage system
after every six inches of timber travel. The average voltage
is fed into the grade decision section after the board has
passed both transducers. Before the board leaves the machines,
it is stamped with a grade. The machine can operate at speeds
up to 1,000 feet per minute, handling two inch nominal lumber
from six to twenty-six feet in length and from a nominal four
to twelve inches wide.

The $13,000 Stress-O-Matic machine is set at a permanent
speed (usually about four hundred feet per minute). Whereas
the CLT-l applies a small load, the Stress-O-Matic machine
applies a much larger proof load. Lumber is fed into the
machine by power rolls. Pressure is applied from above and
fingers underneath the lumber measure calculated deflections
to ascertain the grade. Tests are made in rapid succession,
starting with the strongest 'f' grade (2400f) and progressing

downward by predetermined grade levels. If a piece deflects

5
too much for the stronger grade, succeeding tests are made
until the proper grade is ascertained. This grade is then
stamped on the piece at the out going end of the machine.

Much money and time was spent in the development of
these machines and they are being used commercially at present.
However, visual grading still predominates. Time will be
necessary to answer all questions pertaining to machine grading

and also to educate the users of stress graded material.

LITERATURE REVIEW

Publications discussing stress rating machines first

appeared in 1961. In an initial report by B.J. Hoyle in
June, 1961 (6), results of preliminary tests were presented
for lumber which was stress rated by the CLT-l machine
(Continuous Lumber Tester). Hoyle stated that the test
results demonstrated that moisture content of the board at
time of testing was not critical. He also stated that
temperature changes had little effect on the machine
accuracy but advocated a seasonal change in adjustment.
It was mentioned in this article that the Oregon Forest
Research Center, Washington State University, and Professors
John Howe and Arland Hopstrand of the University of Idaho
had all contributed to the collection, testing, and analysis
of the relationship between modulus of elasticity (MOE) and
modulus of rupture (MOB). The correlation coefficient was
found to be between 0.70 and 0.80.*

In October of 1961 an article (1) appeared in the

Lumberman's Journal entitled "A Positive Stress Rater“.

 

*The correlation coefficient is a unitless indicator
of the association between two variables. A perfect relation-
ship results in a correlation coefficient of 1.00 and a value
of zero for a wholly imperfect relationship. See Appendix I
for further discussion.

7

This report described the early success achieved with the
Western Pine Association's Stress-O-Matic machine. In 1963,
articles (2,3,10) appeared in the Timber Trades Journal and
in the Forest Industries magazine explaining internal mechanisms
and operations whereby the two machines determined stress ratings.
In 1969, L.W. Wood of the Forest Products Laboratory explained
the differences between the two machines and pointed out some
problems of correlation with final strength properties (12).
At this time, he advocated the use of supplementary visual grading.

J. G. Sunley, W. M. Hudson, and W. T. Curry reported on
the research on machine grading in Great Britain (10,11). They
described a prototype at Princes Bisborough which was capable of
grading at speeds in excess of eighty feet per minute. Baltic
Scots Pine and Norway spruce were tested. Data was included
which compared visual and mechanical stress grading with actual
strengths. Sunley and Hudson indicated a correlation coefficient
of 0.836 between MOB as a joist and MOE as a joist. It was also
stated that the correlation between MOB and MOE seemed to be
independent of species. Although these boards were tested in all
four directions, no mention was made about the effect of load
being applied to different faces of the board.

In 1962, J.F. Senft, S.K. Suddarth, and H.D. Angleton of
Purdue University reported test results of static bending tests
on two hundred 10 foot 2 x 6 Douglas fir joists (9). The
specimens were tested over a nine foot span using two point
loading. The report showed a graphic representation of the
simple correlation between MOB, density, MOE, slope of grain,

and moisture content. In this study, the correlation between

8
MOB and MOE was found to be 0.681. These boards were kiln
dried to 10, 15, and 30 percent moisture contents. It was

found that moisture content had little effect on correlations.

PURPOSE

It was the purpose of this study to compare the allowable
fiber stress in bending as Specified by a CLTel lumber grading
machine and as specified by visual stress grades with the values
of modulus of rupture determined in laboratory tests of nominal
2" x 8" Douglas fir joists and planks. Strength and stiffness
properties_of the joists and planks were to be found by placing
increasing magnitudes of evenly distributed load over a ten

foot beam span.

TESTING PROCEDURE

Preparation andigescription of Samples

A total of 150 intercoastal type Douglas fir 2"x8"x12'
boards were secured from a West Coast sawmill. These boards
were taken from regular commercial stock and were graded
before shipment by a CLT-l grading machine. They consisted
of fifty boards each of three machine grades - 1500f, 2100f,
and 2400f.

For every board, all defects including knots, wane,
checks, splits, and pitch pockets were recorded on a grid as
well as the growth ring orientation at one end of the plank.
All four sides of the board were sketched. The knots were
classified according to their narrow diameter in inches, their
type (tight or loose), and the amount of grain deviation around
the knot (mild, normal, or extreme). The depth of the splits
or checks was determined and the area of wane on each face was
measured.

According to ASTM standards (D198-27(2h)), when loading
to failure, the load was to be applied to the poorer of the
loading faces. Since the modulus of rupture was always deter-
mined with the load applied to the bottom edge, the board was
oriented so that the poorest edge was recorded as the bottom
edge when the faces were recorded on the grid.

After all the defects were recorded, every board was

10

11

visually graded according to WCLIB stress grading rules by a
certified lumber grader, Mr. Lynn Gresham of the Detroit
Lumberman's Association.

Prior to the large scale tests, the lumber was conditioned
to a uniform 12 percent moisture content. Conditioning was by
means of a dry kiln with a dry bulb temperature of llOoF and a
wet bulb temperature of 100°F. Subsequently, the boards were
stored in a controlled condition room at 12 percent EMC (69°F
and 70 percent BH). The moisture content of each board was
determined at time of testing as discussed under small scale

test procedure.

Large Scale Test Procedure

Immediately prior to testing. each board was measured
to determine the moment of inertia. Thicknesses were measured
to the nearest 0.001 inches using an Ames caliper gauge
(Figure 1). These measurements were taken at the center of the
wide dimension at three places along the board - three feet
from each end and in the middle of the board. An average
thickness was determined from these numbers. Widths of the
boards (larger dimensions) were measured to the nearest 0.001
inches at the same three positions along the members using a
vernier caliper (Figure 1). These three measurements were
also averaged.

Load deflection characteristics of each board were
determined by means of Special testing apparatus (Figures 2
and 3). The apparatus contained thirteen hydraulic cylinders
to approximate a uniform load over a ten foot span. The

cylinders were located one foot from each reaction point and

12

FIGURE 1.--Method of measuring boards to determine
moment of inertia .

 

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FIGURE 3.--Testing load deflection properties:

(a) as a joist

(b) as a plank.

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17
were then spaced every eight inches. The reaction supports
were two large bearings which were free to rotate but which
were restrained from translation. Two steel plates separated
by roller bearings provided nearly frictionless movement
between test members and supports. Buckling of the test boards
was prevented by two pieces of 2 x 2 angle iron used as hold
downs. These hold downs were supported by metal plates and
roller bearings to prevent friction losses.

The load was measured at one reaction using a Baldwin
SB-A, 10,000 pound load cell when testing as a joist. The
load cells were inserted between the board and the reaction.
Load cell signals went to an Ellis BAM-l amplifier and from
there into one channel of a two channel servo-recorder. The
other channel was activated every 0.100 inches of deflection
to indicate deflection at the different load levels. The
deflection was always measured using an Ames dial gauge at
the middle of the span.

The boards were tested for load deflection character-
istics with load applied to each of the four faces and for
breaking strength with load applied to the narrow face which
contained the most serious combination of defects (bottom edge).

Each board was first loaded non-destructively as a plank
with load applied to the face and then to the beak. (See Figure
4 for direction of load terminology). In both cases. the load
was applied along the length of the board at the'centerline of
the face or back. Before loading, all the cylinders were
brought into contact with the board and the dial gauge was set

at zero. Subsequent loading was applied so that the deflection

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19
was increased 1.9 inches per minute to produce a rate of strain
in the extreme fiber of .00015 inches per inch of fiber length
per minute. The load was applied until the deflection reached
1.500 inches. The load necessary to deflect the plank 1.2
inches was determined by subtracting the load at 0.300 inches
deflection from the load at 1.500 inches deflection. It was
previously determined that within this range, the load deflection
curves were linear and that the proportional limit was not
exceeded.

In determining load-deflection properties as a joist,
the load was applied at a rate to deflect the joist 0.25 inches
per minute to produce a rate of strain of 0.0007 inches per inch
of fiber length per minute. In bringing the cylinders in contact
with the joist, a pre-load of approximately 100 pounds was
applied in each case. The load required to deflect the joist
0.500 inches more than the pre-load deflection was used to
determine MOE. Within this range, the load-deflection curve
was linear.

After the bottom edge was subjected to the load to
produce 0.500 inches of deflection, the dial gauge was removed
and loading was continued at the same rate to failure. The
ultimate load at failure was used in the calculation of the

modulus of rupture (MOB) (Figure 5).

Small Scale Test Procedure

After a test board had been loaded to failure, small
clear samples were cut from it to determine clear wood MOE,
MOB, specific gravity, and board moisture content at time of

test.

20

FIGURE 5.--Testing for modulus of rupture:

(a) under load

(b) failure.

 

 

 

 

22

The moisture content and specific gravity of each board
were determined from two samples. They were taken from clear
wood near the failure. These samples were of various sizes
and shapes and weighed from 35 grams to 110 grams with an
average weight of about 70 grams. Immediately after the
samples were cut from the board, they were weighed and then
placed in an oven to dry. The oven dry weights were recorded
and the samples subsequently dipped in melted paraffin. Oven
dry volumes were determined by the ASTM water displacement
method.

Two 1-1/4 x 1-1/4 x 15 inch beams were also out from
clear wood near the failure to determine MOE and MOB. These
samples were cut with the grain running along the long axis.
After being out roughly to size, they were finish planed to
one inch square and measured to the nearest 0.001 inch using
a micrometer dial caliper. These samples were stored and tested
in a testing room at 69°F and 70 percent BB (12 percent EMC).

The samples were tested for MOE and MOB in a Dillon
testing machine according to instructions for static bending
in Part II, Secondary Method of ASTM D143-52. The reactions
were 3/4 inch radius aluminum blocks. The load was measured with
an SB-U 2500 pound load cell connected to one channel of a two
channel servo-recorder. A fifty pound pre-load was applied to
the sample before the dial gauge was set at zero. Then, load
was applied at the prescribed rate until the deflection equalled
0.100 inches. At this time, the second channel of the servo-
recorder was activated to indicate load at this deflection.

This load (minus the initial 50 pounds) was used to determine

MOE. Loading was continued to failure.

TEST RESULTS

Modulus of Rupture of Boards

The modulus of rupture (MOB) was calculated for each
board after the load was applied to the bottom edge, until
failure was achieved. The joist MOB values ranged from 2,031
psi to 11,700 psi, with an average of 5,856 psi and a standard
deviation of 2,728 psi.

In Figures 7-20 and 2h respectively, MOB is compared
with EMSB grade, visual grade, modulus of elasticity (MOE)
(plank), MOE (Joist), MOE (1500f EMSB), MOE (2100f EMSB), MOE
(2h00f EMSB), MOE (1200f visual), MOE (1500f visual), MOE
(1900f visual), MOE (2050f visual), stiffness, slope of grain,

specific gravity, and clear wood MOB.

EMSB and Visual Grades

The boards were originally machine graded and the
sample consisted of 50 boards each of three grades - 1500f.
2100f, and 2400f. Upon visual grading, these 150 boards were
classified into 43 - 1200f, 70 - 1500f, l9 - 1900f, and 10 -
2050f. In addition to these grades, six boards were judged
defective under WCLIB grading rules and were graded utility.
Due to oversight, the visual grade was not recorded for two
boards.

Figure 6 compares the distribution of the test boards
23

GRADE

VISUAL

2050 f

I900 f

I500!

IZOOf

COMPARISON

 

 

 

 

 

 

 

 

 

 

0 BOARDS I o BOARDS l0 BOARDS
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5 BOARDS 5 BOARDS 9 BOARDS
26 BOARDS 27 BOARDS l7 BOARDS
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l7 BOARDS l3 BOARDS I3 BOARDS
ISOOf 2|OOf 2400 f

EMS R GRADE

GRADE RESULTS

FIGURE 6

BETWEEN VISUAL AND EMSR

 

25

in the visual grades with their distribution in the EMSB grades.

Figures 7 and 8 show how the allowable design stresses
of the EMSB and visual grades compared with the actual strength
as shown by the calculated MOB. The three EMSB 'f' grades are
broken down in Figure 7 in order to show the number of boards
within each 'f' group that failed at different MOB levels. In
each of the three 'f' grades, the X axis represents the MOB
separated into 500 psi sections. The height of the bars show
the number of boards within a grade that failed within a
particular 500 psi MOB range. Within the 1500f grade, the
average modulus of rupture was u,265 psi with a standard deviation
of 1,828.6 psi; within the 2100f grade, the average MOB was 5,06h
psi with a standard deviation of 1,982 psi; within the 2h00f
grade, the average MOB was 8,16h psi with a standard deviation
of 2,568 psi. The MOB range is shown on the bar chart.

The four visual stress grades are broken down in Figure
8 with the same purpose and procedure as in the previously
mentioned figure. Within the 1200f grade, the average MOB was
n.8u2 psi and the standard deviation was 2,u02 psi; within the
1500f grade, the average MOB was 5,429 psi and the standard
deviation was 2,453 psi; within the 1900f grade, the average
MOB was 7,129 psi and the standard deviation was 2,396 psi; and
within the 2050f grade, the average MOB was 10,035 psi and the
standard deviation was 1,858 psi.

Not shown on this graph but also calculated was the MOB
of each of the six boards graded utility. The MCB values
ranged from 3,206 psi to 11,062 psi with an average of 6,582

psi.

26

Modulus of Elasticity

The MOE was calculated as a plank with load applied to
face and back and as a joist with load applied to top edge and
bottom edge. The MOE with load applied to face was used to
represent the plank MOE instead of averaging MOE (face) and
MOE (back) to avoid the possibility of a test from one side
affecting a test from the opposite side. Also, the MOE with
load applied to top was used to represent the joist MOE for
the same reason. Furthermore, the two values of MOE as a
plank compared well with each other and had a correlation
coefficient of 0.98. Similarly, the two values of MOE as a
joist were also close and had a correlation coefficient of
0.97u.

In Figure 21, the plank MOE was compared with the
joist MOE. The plank MOE values ranged from 1.183 x 106psi
to 2.515 x 106psi with a mean of 1.6fl9 x 106psi and a

standard deviation of 0.311 x 106psi. Also, the joist MOE

6 6

values ranged from 0.908 x 10 psi to 2.352 x 10 psi with a

mean of 1.u21 x 106psi and a standard deviation of 0.299 x 106
psi. Calculations show a correlation coefficient of 0.9200
between MOE plank and MOE joist.

In Figure 9, the joist MOB was compared with the plank
MOE calculated with load applied to the face to illustrate the
correlation between the two variables. The correlation coeff-
icient was found to be 0.6951.

Points were also plotted to Show the relationship
between joist MOB and joist MOE. This relationship is found

in Figure 10. The correlation coefficient between these two

27
variables was found to be 0.7096.

In Figure 23. the MOE values calculated as a plank are
plotted against the clear wood MOE for each board. These two
variables had a correlation coefficient of 0.7750

Also, in Figure 23, the plank MOE values were plotted
as a function of specific gravity. A correlation coefficient

of 0.6374 resulted.

S iffness Properties
The stiffness was calculated for each board by multi-
plying the plank MOE by its corresponding moment of inertia

at time of test. These stiffness (or EI) values ranged from

6psi with a mean of 4.2110 x 106psi

and a standard deviation Of 0.7454 x 106psi.

3.090 x 106psi to 6.207 x 10

In Figure 18, the MOB values of the boards were plotted

against the El values with a correlation coefficient of 0.7030.

glgpe of Grain

The slope of grain was measured on the back for all
boards but only 50 boards had a measured slope. For these 50,
the slope of grain ranged from one inch in 48 inches to one
inch in eight inches with an average slope of one inch in 15.6
inches.

Previously mentioned plank MOE was shown as a function
of Specific gravity in Figure 22.

In Figure 26, the clear wood MOB is compared with specific
gravity in Fighre 27. The correlation coefficient between
these two variables was 0.6049.

In Figure 20, the joist MOB was plotted against specific

28

gravity with a resulting correlation coefficient of 0.4683.

Specific Gravity

Two clear wood samples were taken from each board to
determine specific gravity. These specific gravities ranged from
0.35 to 0.61 with an average value of 0.464 and a standard
deviation of 0.048.

In Figure 20, the joist MOB was shown as a function of
specific gravity with a resulting correlation coefficient of
0.4683. When plank MOE was compared with specific gravity in
Figure 22, the correlation coefficient was found to be 0.6374.

In Figures 26 and 27 the clear wood MOB and MOE were Shown as

a function of specific gravity.

Clear Wood Modulus of Elastigigy

MOE values were calculated from tests using two clear
wood beams from each board and the average between the two
values was used as the clear wood MOE for that board. The

6 6

clear wood MOE ranged from 0.935 x 10 psi to 2.054 x 10 psi

with an average Of 1.405 x 106psi and a Standard deviation
of 0.224 x 106psi.
The plank MOE was shown as a function of clear wood

MOE in Figure 23 and the clear wood MOE was compared with

specific gravity in Figure 27.

Clear Wood Modqlus of Rupture
The same two clear wood samples used to determine MOE
were used to determine clear wood MOB and the average between

the two was used to represent the clear wood MOB for the

29
board. The clear wood MOB values ranged from 8,273 psi to
15,529 psi with an average of 11,628 psi and a standard
deviation of 1,562 psi.

Figure 25 shows the previously discussed relationship
between clear wood MOB and clear wood MOE.

The clear wood MOB was compared with specific gravity
in Figure 26. The two variables had a correlation coefficient
of 0.7401.

In Figure 24, the MOB of the board containing defects
was compared with the clear wood MOB. Calculations resulted

in a 0.5552 correlation coefficient.

Moisture Content

The same two clear wood samples from each board that
were used to find specific gravity were used to determine
moisture content at time of test. The moisture contents
ranged from 11.0 percent to 12.9 percent with an average of
11.84 percent.

The moisture content of the small clear sample was also
determined. A representative 23 samples were tested with a
range of 11.5 percent to 13.7 percent and an average of 12.4

percent.

 

Standard

Standard eror

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Comparison Between Mean Deviation R R‘ of Latimatc chression Equation
, NOR and 5855 7 2728.3 1,907 9
............ 0.0951 0.4832 ------- MOR . 0.00009IIMOLI - 4192.2
MOE as a Plank I 049 0 3113 ‘
14011 and 5855.7 2728.3 1 928 7
........... 0 ------ 0.7090 0.5030 -——---- MOR . 0.000404IMOII - 3331.7
MOI: as a Joist 1.4211 x 10 0 2995 1
Clear wood MOR 11,028.4 1501.5 835.09 I
................ 0,3401 0 7159 ---.-- NOR - 0.005895(PHNJ . 3343.5
and Clear Wood MOE I 405 x 10° 0.2241
Clear wood MOE I 405 x 10° 0.2241 1797 ( 0
................. 0,0049 0,3659 --~-- MOE a 2.8200 x lU‘ISpeciflt Grav.) 0 .0952 x 10
and specific Gravity 4044 0.0482 I
I
Clear Wood MOR 11,030.2 1,500.0 1,057.1 ;
--------------- 0.7401 0.5477 ------- MOR - 24,047.3(Spcciflc Grav.) 0 403.6 I
and Specific Gravity .4044 0.0482 '
Aj
Joist NOR and 5,855.7 2728.3 2,270 9 I
.............. o 5552 0.3082 -—----- NOR . 0.9700(C.N. MOR) - 5,423.3
Clear 8004 won 11.028 4 1501.5 I
I
Joist NOR and 5,855.7 2728.3 2,417.9 ,
............. 0.4683 0.2193 ------- MOR I 20,486(Spccif1c Grav.) - 6,424.4 I
Specific Gravity 4644 0.0482
IJoist HOR and 4,204.7 1828.0 1,701.8
- ---------------- 0.3898 0.1519 ------- MOR = 0.005346(MOE) - 3103.1
Plank HOE (lSOOEMSR) 1,379,000 133,300 I
I
IJoist NOR and 5,004.2 1,982 4 1,930.9 I
................ 0,2540 0.0048 -----_- MOR . 0.00319(MDE1 - 208.0 I
Plank MOE (ZlOOEMSR) 1,588,500 157,071 .
I
onist won and 8,100.5 2,508.1 2,109.0
. ................ 0.5482 0.3005 ....... MDR = 0.005381M0E) - 2,429.8
Plank MOE (2400EMSR) 1,909,824 201,808 -
NOR and 5984.8 2,728.2 2,740.3
............. 0 1032 0.0117 ------- MUR . 1.188(SLOPh) . 0,741.4
Slope of Grain 1/15 D l/40.3
MOR and 5855.7 2,“28.3 1,940.9
................ 0.7030 0.4942 --—---- MOR s 0.002$7(El) - 4978.7
,Sriffness (E1) 4,211,040 745,408
Plank Elasticity and 1,649,440 311,324 197,391
................ 0 7751 o 0007 ------- MOE (PLANK) . 1.0700(c.w. MOE) . 130,425
Clear wood MOE 1,405,353 224,121
Plank MOE and 1,049,440 311,324 22,404
................ o 9200 0.8905 ------- MOE (PLANK) = 0.9504(MOP JOIST) . 290,300
‘Joist MOE 1,421,113 299,477
MOR and 4,842.9 2,401 7 1.805 9
................ 0.0093 0.4480 ------- M08 x 0.00579(MOE) - 4,291
MOE (1200f Visual) 1,570,72 277,481
NOR and 5,429.5 2,453.3 1,811 2
I ---------------- 0.0803 0.4029 -------- MOR . 0.00577(MOE) - 3,802.1
MOE (1500f Visual) 1,011,271 289,438
!Joist NOR and 7,129.0 2,395.6 2,199.9
. ---------------- 0.4512 0.2030 ....... MOR = 0.0030(MOE) . 1,440.7
IPlank MOE (l900f Visual) 1,722,737 327,343 i
I
Joist MOR and lo 035 3 1,857.9 1,908 5 I
I ---------------- 0.0405 0.0022 ------- HDR . 0.00038(MOE) . 9,233.2 I
Plank MOE (2050f Visual) 2,101,000 220,158 1
I
I I
Plank MOE and 1,049,880 312,320 .41,479 '
! ---------------- 0.0374 0.40h3 ------- HOE r 4,128,774 (Specific Grav.) — 207,301
Specific Gravity 4044 0482
IPlank MOE (Face) and 1,049,440 311,324 02 520
---------------- 0.9798 0.9599 —-—---- MOE (FACE) - 0.9754 11k“; BACK) . 28,750
(Plank MOE (Back) 1,001,547 312,715
L _
Joist MOI (Top) and 1,429,293 290 838 07.2'9
................ 0 9742 0.9491 ------- MU! (TOP) = 0.9074 IAIN. NJIIUHI . 39,345
Joist MOE (Bottom) 1,430,571 298,922

 

ARE

NUMBERS ON HORIZONTAL SCALE

LOWER END OF SOOpsi

RANGE.

"I‘

I 2

Hr"

I01-

2400f

7+

 

 

 

E
C
N
E
D
F
%% N
xx. 0
C
o.
A? A
)0: o
5
.009
O
a;
s...
E
f. %% mm f.
O 0; CU O
O l
O 500 m 0
l I I-IR
2 O E PMIV
EW
m.0
LL
nuN
E
Tm
TS
OE
DD
£— _ FL. _h_h__hb
.344 _ «na_dq-dqana
Q10 210987654321
anew—0 U<u 2.1:; mamdom “.0 mmeDz

 

EMSR GRADE VS MOR

 

7

FIGURE

OF BOARDS WITHIN EACH GROUP

NUMBE R

O—NUDUIOSNGJ

o-NUAumqm

O-Nutbulmflm

IL NUMBERS ON HORIZONTAL SCALE ARE
“ LOWER END OF 500psi RANGE.

,1 20501

 

 

 

 

 

.000
MOR IN 500081 GROUPS 0 O
VISUAL GRADE VS MOR

FIGURE 8

AS A JOIST

(0“)

BOARD MODULUS OF RUPTURE

zqmm
Iepoo
IBpoo
Izooo
|6poo
15900
Imooo
Imooo
IZfiMO
Ihooo
10000
9000

0000

I

-_-..

T

_”T

I-
I
I
I

I

1..
I

I
I,_.
I

I
5_
i
I
I

I
:1.
I
I

I
?__
I
I

zoooL

8000;.
I

5000

aooo

1000

2poo
0000

O

',,_

-- 2.1----”

I———

 

Ljal
1.0

OBSERVATIONS 3 I50

R=.695|

R2 =.4B32
REGRESSION EQUATION:

MOR = 6.09l7x I03 (MOE) " “92.2

0 . 9
. O
/
O . .//
° /
O o /
o /
. /
/
/
I
. I
/
. e . /
/
l .
/ 0 o
/
o I
/ o
/' ° 0
0 /
' /
O
x/ ' .
/
/
e O//..o
o 0 ; 0 ° .
I
o 09' 0 °
0 I 0
° /. o o
O 0
e / o
./ O. .
. I
e
o
. //.O O . O .
I 0 o. o e
I 0 .°
I O o 0
I e . °. .
I o . 0 O

IILIIIIIIIIIIII
l.l I.2 l.3 1.4 1.5 1.6 1.7 1.8 1.9 2.0 2.1 2.2 2.3 2.4 2.5

BOARD MOE (IO ps1) As A PLANK
JOIST MOR VS PLANK MOE
FIGIJREI 9

20,000__

 

 

19,000 __
18,000 2
17,000 __ OBSERVATIONS = 150
R = .7096

I O Er.

6,00 122:.5035
515,000. __ REGRESSION EQUATION!

6 M 0 11:69.5» x 10511105) — 3331.7
514,000 __

<

«313.000 ,__.

<

312,000 _

m . O o
e ' .-

11,000 _._ . ,- /
m . ° / .
m ' o o ' //
=10,000__ - /

1- ° /
CL 0 ’ /
D /
a: 9,000_, . - , . //
o ' / .
g 8,000_ // . .
o O .. . /
o ' . )/ 0
13 7,000,__ - ° -° -. /// .
.1 . /’
D
69000 0 . o . / o .
8 I-—— 0 o o o 3:... .0
2 . I, °

5,000,— . g .’ o . . o
o o o. / . .0 o
C 49000 *—- //I. . . o
:0 .° ,°° .” .' . . "

3'000 L, /.I .0. . g . co . :

2.000___' °. 00 :O.

"COOL.
o _.4 I I 1 1 1 I 1 1 1 1 1 I 1 1 1
10 1.1 1.2 1.3 19 1.5 1.6 1.7 1.8 1.9 2.0 2.1 22 2.3 2.4 2.5

BOARD MOE (IOGpsi) AS A JOIST
JOIST MOR VS JOIST MOE

FIGURE 10

AS A JOIST

W“)

BOARD MODULUS OF RUPTURE

20,000

10000

18,000

IzOOO

18000

13000.

1&000
13000
12000
ILOOO
“x000
%000
8000
zOOO
8000
3000
«000
3000
2000

“000

 

I
12

OBSERVATIONS = 49

R: .3998

2

R =4519
REGRESSION EQUATION:
MOR = 5.3461 :1 163114015) - 3103.1

1 I
13

1.4

I l
15 LG

L
1.7

I
1.3

I i I I I 1 I
1.9 2.0 2.1 2.2 2.3 24 25

BOARD MOE (106psi) AS A PLANK

MOR VS

IMCDE

WITHIN

FIGURE

1500f EMSR GRADE

AS A JOIST

(psi)

MODULUS OF RUPTURE

BOARD

20,000...
19,000 ._.

18,000.-
OBSERVATIONS: 50
'1000 — R=.2548
R = .0848
REGRESSlON EQUATION:
15,OOO_. MOR =3.3189x163(MOE)—- 207.95

16900,

14000 _
13000.

12,000 ,_
11,000 _
10,000 __
9,000 ._
8,000I.
7,000
8,000 _ .°
5000 ,. .

4,000 ._

3,000_ ' H: ,

2,000 _

1,000

.-

 

0 .r I I I I I L I 1 1 I I I 1 1 I 1
1.0 1.1 1.2 1.3 1.4 1.5 1.8 1.7 1.8 1.9 2.0 2.1 2.2 2.3 2.4 23
80AR0 MOE 1106mm As A PLANK

MOR VS MOE WITHIN 2100f EMSR GRADE

FIGURE 12

 

AS A JOIST

Wu)

MODULUS OF RUPTURE

BOARD

20,0001-

19,000

18,000 ._
17,000 ._
18,000 ._-
15,000 ._
14,000 E
13,000 __
12,000 ._
11,000 _
10,000 _
9,000 __
8,000 _
7,000...
8,000 _.

5,000 _

4,000

3,000

2,000...

1,000 ,__

 

b—n

OBSERVATIONS = 51

R=.5482
R2=.3005
REGRESSION EQUATION:

MOR 3.3783 111631MOE1— 2429.8

1 I I l I 1 I I I I 1 1 I I L
Li I.2 L3 L4 I5 l6 I.7 LB I.9 2.0 2’ 2 2 2.3 2.4 2.5
BOARD MOE (IO psi) AS A PLANK

MOE WITHIN 2400f EMSR GRADE

FIGURE

VS

l3

BOARD MODULUS OF RUFTURE (psi) AS A JOIST

20000.

19000

18000

D...

17000

18000
15000.-
14,000...
13000

y—-

12000

p.-

H000

p—

10000

p...—

9000..
8000
2000
@000
3000
4000
3000..

2000

1000

_

 

MOR VS MOE WITHIN

0 “EI l I I I I I

OBSERvAnONs=43

R=.6693

R2=.4480
REGRESSION EQUATION:

MOR==3793xIO31MOEI - 429L6

I 1 I I I I I I I
17 L8 19 20>21 22 23 24:15
AS A PLANK

1200f VISUAL GRADE

1.0 1.1 1.2 1.3 1.4 1.5 1.6

BOARD MOE (10 psi)

FIGURE I4

AS A JOIST

BOARD MODULUS OF RUPTUREIDSI)

20000

19000.

18000

17000

18000.

15000

14000

13000.

12000
17000
10000
9000
8000

7000

8000.

5000

7000.

3000
2000

7000

——

OBSERVATIONS=7O
*“ R= .6803

R2: .4629
REGRESSION EQUATION:

MOR: 5.7881116311111051- 3882.0

 

LI 1 I I I I I I I '1 I I I I 1 I
1.1 1.2 1.3 1.4 1.5 1.6 1.7 1.8 1.9 2.0 2.1 2.2 2.3 2.4 2.5
BOARD MOE 1106mm AS A PLANK

VS MOE WITHIN 1500f VISUAL GRADE

FIGURE 15

AS A JOIST

WM)

OF RUPTURE

BOARD MODULUS

29000.

19000
18000
17000
19000
15000
14000
19000
12000
17000
10000
9000
9000
7000
8000
9000
4000
9000
2000

1000

MOR VS

P

 

WEI

1.0

OBSERVATION =

R=.4mz
R2=.2036
REGRESSION EQUATION:

MOR = 3.301xl-031M0E1 "1' 1440.7

19

I I. I I I 1 I 1 I I I I .J 1 I_
u 12 L314.15 u517'18 L9 202m 22 23:2425

80AR0 MOE (1061131) 115 A PLANK

MOE WITHIN 19001 VISUAL QRAQE

HGURE 16

AS A JOIST

(psi)

BOARD MODULUS 0F RUPTURE

20000

19000

19000

17000.

16,000 _

19000
14000
13000
12000
17000
19000
9000
9000
7000
8000
9000
9000
9000
2000

1000

p.—

r—

—

—

_—

P

I—

—

—

 

MOR VS

NLI
1.0

1.1 1.2

OBSERVATION =

R=.0465

R2=.0022
REGRESSION EQUATION:
MOR = 3.8188 111.04 (MOE) +

10

9233.2

1 I 1 I I I I I I 1 I I I 1 I
13 14 15 u517 18 19 2020 221n524»23

BOARO MOE 11051111) As A PLANK
MOE WITHIN 2050f VISUAL GRADE

FIGURE 17

AS A JOIST

OF RUPTURE (psn

MODULUS

B OARD

20,000
19000
18000
17000
18000
15000
14000
13000
12000
11000

10000

9000‘

8000
7000
8000
9000
4000
9000
2000

1000

 

OBSERVATIONS = 150

R = .7030

R2=4942

REGRESSION EQUATION:
MOR = 2.572911103IEI) —- 4978.7

/
/
/
/
/
/
. 0 0 . /
0 /
0 . I
0 . 9 . /
0 0 0 /
° 0 ' /
. ° /
/
' 0 /
/
0 0 ' /
0 ° . /
/
0 0 / °
/ ' ’
0 ° /
0 . .../
Q. 0 O O /. ....
0 0 l
0 /. . 0
,0
0 . /
O 0 ./ .
’ o "' :/.'..°: . 0
0/ .
0 .0 .;’. . 0 0
‘ 0. I .
'/ 0' 0
/
. 0/ . 0 O
0 /.. 0 CO 0
00: 0. .
I0 00 ..
/ .' o .0. 0
/ 00 0.
O: 0 . o
I...
LA 1 1 I 1 ' I I 1 1 I

 

3.0 3.5 4.0 4.5 5.0 5.5 8.0 6.5 7.0
El (106981) AS A PLANK

JOIST MOR VS STIFFNESS (EI)
FIGURE 18

(psi) AS A JOIST

OF RUPTUR E

BOARD MODULUS

20,000 .

19000
19000
17000

18000
15000
14000

13000

12000.

17000
10000
9000
8000
7000
8000
5000
4000
3000
2000

7000

 

OBSERVATIONS = 50

R:- -.1082
R2: .0117
REGRESSION

MOR:

EQUAHON:

-11884.0 (SLOPE) ‘1' 6741.4

-.
*5
~~

I I I I I 1 I I

20 14.3 11.1
SLOPE 0F GRAIN (IN/1N)

1
_I_
9.1

JOIST MOR VS SLOPE OF GRAIN

FIGURE 19

(psi) AS A JOIST

0F RUPTURE

MODULUS

BOARD

20000
19000
19000
17000
19000
19000
19000
19000
12000
17000
10000
9000
9000
7000
8000
9000
4000

9000

2000-

7000

JOIST MOR VS SPECIFIC GRAVITY

7..

 

 

._ OBSERVATIONS =149
R=.4683
“" R2=.2193
_. REGRESSION EQUATION:
MOR: 26486.7 (SPEC. GRAVJ- 6424.4
/
I—l,’/ - 2. ° . E '
ArIIIIIIIIIII1L1114III-‘IIIII
.35 .37 .39 .41 .43 .45 .47 .49 .51 .53 .55 .57 .59
SPECIFIC GRAVITY

FIGURE 20

AS A PLANK

BOARD MOE (10 psi)

 

7.111

OBSERVATIONS = 150
R=.9200
Rz=.8463

REGRESSION EQUATION:

MOEIPLANKI

1 I
1.01.1 1.2 1.3 1.4

BOARD MOE

= .9654(MOE-JOIST) + 290311106

1 1 I I 1 I I 1 1 1 1
1.5 1.6 1.7 1.8 1.9 2.0 2.1 2.2 2.3 24 2.5

(10611111) As A JOIST

PLANK MOE VS JOIST MOE
FIGURE 21

PLANK

AS

BOARD MOE (10 psi)

2.5

2.4

2.3

2.2

2.1

2.0 _

1.8

1.7

1.6

1.5 .

1.3

1.2

1.0

 

.35

I

0 /
/
/
/
I
I
. /
/
/
. /
O [I
. 0 /
/0
0 ’ o . ,
0/ 0
0o l”
/
O . /.
° /
/
. /
s /’
0 ./
’0
0
O I
. 00 I.
. /
0’ °
/ 0
/\ .
' I :0
I
0
0/ . 0 fl 0
O ./.
/ 0
l.
/
. .
I 0
I. 0 ’
/ S .
/ . Q 0 O
I O . .
/
/ 3
I
/ 0

OBSERVATIONS = 150

R = .6374

R28 .4063
REGRESSION EQUATION:

MOE = 4.128811106 (SPEC GRAV) - .267411106

IIIIIIIIIIIIIIIIIIIIIIIII
.37 .39 .41 .43 .45 .47 .49 .51 .53 .55 .57 .59 .61

SPECIFIC GRAVITY

PLANK MOE VS SPECIFIC GRAVITY

FIGURE 22

1106 psi) AS A PLANK

BOARD MODULUS OF ELASTICITY

2.7

2.6

2.5

2.4

2.3

2.2

2.1

2.0

'0'

1.0

 

 

F-
._ OBSERVATIONS =150
R=.7750
”“ R2: .8007
__ REGRESSION EQUATION: .
o I
MOE=LO7661CLEAR MOE) + 0.136411106 //
._ /
/
/
L- /
/
0 /.
r-— ’. /
/
/ 0
—— O //
00 °./
__ 0 g/l . .
/.
1__ /' 0
O //
1— ° /0
0 /:
_ /. 0
C /0. 0
*— LI’ .
/
00 /.0 ‘
>——- /..
/.:
I- 0/ 0
0 //0 0 . .
_ °'// 0 0
0/ g
/
II
I
7,, iIIIIIIIIIII
. 1.0 1.1 1.2 1.3 1.4 1.5 1.8 1.7 1.8 1.9 2.0 2.1

CLEAR WOOD MODULUS 0F ELASTICITY (1061351)

PLANK MOE VS CLEAR WOOD MOE

FIGURE 23

BOARD MODULUS 0F RUPTURE (psi) AS A JOIST

20000
19000
18000
17000
18000
15000
14000
13000
12000
N000
19000
9000
8000
7000
8000
5000
9000
9000
2000

1000

 

 

I-—-
OBSERVATIONS = 150
— R = .5552
R2=.3082
1——
REGRESSION EQUATIONz
.... MOR = .9700 (CW. MOR) .. 5423.3
/
/
__ /
O . C . //
0 0 /
I— /
. /
0 0 /
0 /
I-— 0 //
I
/
+— /
0 /°/
_ ./
-.:%,Q’
0 // ' .
. .3 04p .
1.. ° /. . o
/ O
I . o
— / ° 0 0. o
/- ', ,
>—— // . ..
9000 10,000 12,000 14,000 18,000 18,000

CLEAR w000 MODULUS OF RUPTURE (psi)
JOIST MOR VS CLEAR WOOD MOR

FIGURE 24

(pan

RUPTURE

MODULUS OF

190001...
I
I
18,0001,_
1
I
170001_
1

18,OOOI__

15,000I,_

1

14,000?

13,000'._
I

1

120009.
17000.-
10,00 0:..-
9009” ,

0001

(P

8

70002-
6,000I._
90002-
90001
90001-

2,000f..-
1

70001-
I

0 1+4---..I

.9 IO

IREGRESSION

_-I._ -L ._4_...1__.4_ I I. I

0 [I
.’
I
l
'/
I
. /
I
. .‘O 0’ .
0 . I
.0 ° ’1 0
0 ° ‘, 0
. I
0 ' ' I
. Q
’.0 . '0 0
. I
.0 I O.
‘ . 0 0 I 0
0 .. . . 0
0
0 I”
0.. 0 .
0’ p.
I . o O O
000 0‘. 0
.0 ' 0 0
. ‘0. 0 ’ .00
0 0
0 .. . ‘.(.. 0 0
O/ O . . Q
0
0
0 0’0 .0. ‘
I . 0 1 0 °
00"... .
I
I .. ’ 0
0 0
.0
'0 0
0

OBSERVATIONS=15C>
R=.B461

R2=.7159

EQUATION:
MOR = 5.895 x 163(MOE1 + 3343.0

I. .L

11 12 L3 L4 15 16 L7 L8 L9 21)

6 .
MODULUS 0F ELASTICHY H0 05”

c EARINOOOMMOR VS CLEAR MOE

FIGUR E 25

(psi)

MODULUS OF RUPTURE

20000
19000
19000
17000
18000
15000
14000
13000
12000
H000
10000
9000

9000

7000.

9000
9000

4000

9000

2000

100%_

r—
I—- 0 0 : ///
I‘ . . ',-./
0 .. 0/://. . .
0 0 . :./,/. :. 0 o 0

r_ . ,l’tz 2: . 0 0
' y’i 1 ° . °
—— /’/. °
_ OBSERVATIONS = 149

R=.7401
— R2=.5477
f‘ REGRESSION EQUATION!

MOR =24047.3 (SPEC. GRAV.)+ 463.6

 

O

 

'I 1 1 1 1 1 1 1 L 1 1 1 I 1 1 1 I 1 1 1 1 1 1 1 1 1
.35 .37 .39 .41 .43 .45 .47 .49 .51 .53 .55 .57 .59
SPECIFIC GRAVITY

CLEAR WOOD MOR VS SPECIFIC GRAVITY

FIGURE 26

(106 psi)

EIJASTICITY

MODULUS OF

2u4

 

 

2.3,._
2.2 _ OBSERVATIONS =149
R=.8049
2.1,_ R2: .3859
1
g REGRESSION EQUATION: .
2.0 I- MOE = 2.8206x10 (SPEC. GR.) + .0952
I
! O
19 I— ,
I
1.8 I,__ ‘ . /
L7 L- ' . ° ,,//
. . . /
1.6 g . . ' . ./,/
! 0 . :// 0 .
I. I ' . ’/ g 0
5 r- : /'
1 ° -- x .
I ' /.
'41— 1. , ,/-
I3 I._ :/.// :0 z .
I z,/ . .
I /I '
12 2.. ,’ g I : . ’
ii I, 0 ° 2
1.. b—. 0

. --.—.—_.—..._.

10
1

IALIIIIIIIIMIIIIIIIIIILIIII

"

.35 .37 .39 .41 .43 .45 .47 .49 .51 .53 .55 .57 .59

SPECIFIC GRAVITY
CLEAR WOOD MOE VS SPECIFIC GRAVITY

FIGURE 27

DISCUSSION OF RESULTS

Statistical analyses were made of the test data for
interpretation of the results. Each individual set of data
was analyzed by showing its range, average value (or mean),
and the standard deviation about the mean. In each graph
plotted, one variable is shown as a function of another.
Where applicable, 8 calculated line of regression shows the
relationship between two variables and the standard deviation

of the points (standard error of estimate) about the line of

stand,error est?)

regression. The correlation coefficient (B =vg- stand. devf

was used to compare the goodness of fit of the data to the line
of regression from one relationship to that of another relation-
ship. The closer R is to 1.00, the better the fit of the data ‘
to the line of regression. If R is squared (to obtain R2 a
correlation of determination) and then multiplied by 100 percent,
the resulting percent will indicate the percent variance in
values on the Y axis associated with the variance of values on
the X axis. For further information see Appendix I.

In Figure 6, the way in which the two grading systems
graded the boards is shown by a matrix. It was evident that
the two systems did not rate the same boards the same° For
instance, of the boards graded 1200f by visual grading rules,
17 boards were rated 1500f, 13 - 2100f, and 13 - 2400f by the
CLT-l machine.

52

53
On the other hand, of the 10 boards that were classified

2050f by the visual rules, all were rated 2400f by machine
grading. This was most likely due to the fact that the wood
was nearly free of defects in this category and both systems
would yeild high f-grades.

The accuracy of the EMSR grade and of the visual grade
in predicting the ultimate strength of the board was shown in
Figures 7 and 8 respectively. It is difficult to say which
method predicted the ultimate strength most realistically
because neither system was accurate. The machine is designed
and set so that, within a 95 percent confidence interval, the
boards will have a 2.1 safety factor. The dotted line in
Figure 7 indicated the lower threshold limit for 95 percent
confidence. It can easily be seen that more than 5 percent
failed below these limits. A total of six boards (2 - ZhOOf
and h - 2100f) failed below the design stress with no safety
limit.

Although none of the visually graded boards in Figure 8
failed below their design stress, more than 5 percent of the
boards failed below the threshold limits for a safety factor
of 2.“. This is true especially in the 1500f group where about
19 boards out of 70 failed below the design threshold limit.

Since the machine grading for 'f' grade is based upon
an assumed correlation between MOR and MOE, these two variables
were compared in Figures 9 and 10.

Figure 9 compared the Joist MOR with the plank MOR.

In determining the 'f' grade, the CLT-l machine flexes the

board as a plank. The scatter diagram shows a rather poor

54
(0.6951) correlation between joist MOR and plank MOE. Since
the correlation between clear wood MOR and clear wood MOE is
much better (0.8h61), the poor correlation found in the
boards must be due to the influence of defects.

The R2 (coefficient of determination) shows that less
than half of the variance in MOR can be attributed to a
variance in MOE. Also, the standard error of estimate of
1,967.9 psi indicates another relationship. Within a 95
percent confidence interval for these boards, the average
value of MOE (1.649 x 106psi) could only predict that the
MOR would be between 1,919.9 psi and 9,791.5 psi.

The joist MOR was plotted against the calculated joist
MOE to determine whether or not a closer correlation would
exist since MOR was determined as a joist. Figure 10 illus-
trates that there was no significant increase in correlation
by measuring MOE as a joist.

In Figures 11, 12 and 13, the joist MOR was compared
with plank MOE within each of the three machine grades to
determine whether or not the correlation was better between
the two variables at the higher 'f' rating. These figures
indicated that the correlation was not substantially better
in any of the grades.

More importantly, these same three figures also
illustrate the capability of the machine to separate the boards
into MOE groups. As shown in Figure 11, the boards within the
1500f group ranged in MOE from 1.15 to 1.60 x 106psi. Those
in the 2100f group (Figure 12) ranged from approximately 1.35

to 1.80 x 106psi. Those boards in the 2400f group (Figure 13)

55
had MOE values greater than 1.60 x 106psi with the stiffest
board reaching 2.50 x 106psi.

In Figures 14 through 17, the joist MOR was plotted
against the plank MOE for each of the four visual grades.
These figures show that the visual grades do not predict
MOE.

In flexing each board, the machine measured the load
necessary to deflect the board a specific amount. The amount
of load necessary determined the machine's MOE rating for the
board. This was only possible because the sizes of the boards
were assumed constant. If a board had been substantially
undersized, the stiffness would have been low even though the
MOE could have been high. For this reason, the stiffness (EI
product) at time of testing was also used to predict MOR in
Figure 18.

Because the boards varied in thickness and height along
the boards, the I values could not be determined as accurately
as the 0.001 inch vernier caliper indicated. However, because
an average of three values was used, the dimensions were accurate
within 1 0.010 inches and the oversized and undersized boards
were discernable.

The results in Figure 18 show that MOR was not better
correlated with stiffness than with plank MOE indicating that
the variance in sizes at time of testing did not help or hinder
the machine's ability to predict MOB.

The slope of grain was measured and its effect on the
joist MOR was shown in Figure 19. In an unpublished paper

entitled "Grading Machines Measure the Effect of Grain Slope"

56

by C. Glover, B.J. Hoyle, and D.V. Woodruff, it was stated
that the slope of grain definitely affected both the MOE and
the MOR of their samples (clear wood). However, because of
the overriding influence of other defects, the slope of grain
had almost no effect on the ultimate strength of the 2 x 8's
in this test. Even boards with slope of grain as high as one
inch in eight inches attained MOR values as high as 8,000 psi.

Joist MOR was shown as a function of clear wood
specific gravity in Figure 20. The scatter diagram indicates
almost no correlation between the two variables.

The strength of clear wood has little to do with the
strength of the boards containing defects as shown in Figure
29 where the joist MOR was plotted against the clear wood MOR.

The fact that slope of grain, specific gravity, and
clear wood MOR have little effect on board MOR emphasizes
the overriding influence of defects on the ultimate strength
of the boards.

Figure 23 showed that the MOE of the boards was less
dependent on defects than was MOR. In comparing plank MOE
with clear wood MOE, the correlation coefficient was found
to be 0.7750. Although this is not a good correlation, it
does show that board MOE is more dependent upon clear wood
MOE than board MOR (H . 0.5552) is dependent upon clear wood
MOR.

Figure 25 supported the long established fact that
clear wood MOR and clear wood MOE are well correlated.

The moisture contents at time of test were found to be

between 11.4 percent and 12.8 percent with an average of 11.8“

57
percent. These results indicated that the difference in

moisture contents at time of tests were small enough so

that they should not have affected the results.

CONCLUSIONS

The two stress grading systems used, EMSR and Visual, did
not rate the boards the same. An exception to this is in
the highest grade where defects are at a minimum and both
systems rated the same boards with the highest f grade.
Neither method proved more reliable in predicting the
ultimate strength of the board.

The machine graded boards did not achieve the 2.1 design
safety factor. Some of the visual graded boards also
failed below their 2.9 design safety factor.

The correlation coefficient between joist MOR and plank
MOE was found to be about 0.70. This correlation was not
improved by measuring MOE as a joist to predict joist MOB.
Using stiffness (EI product) to predict MOR did not result
in a better correlation than using MOE to predict MOR.
Machine grading did separate the boards into MOE groups
while MOE seemed independent of visual grade except in
the high f grade.

With this sample, the slope of grain, clear wood MCR,

and density had little affect on the ultimate strength of
the 2" x 8" boards.

E as a joist correlated very well with E as a plank.

E is a better indicator of modulus of rupture than is

specific gravity.

58

APPENDIX I

Statistical Methods Used

In this investigation, statistical analyses were made
in order to determine the association between measured and
calculated variables for each board. Statistical determination
of the relationship between variables, dispersion, and degree
of correlation of the experimental data were also made. The
relationship between independent and dependent variables was
statistically evaluated in simple regressions. (Extensive use
of the Control Data 3600 digital computer operated by Michigan
State University was made to compute the regressions and related
statistics. Programming was simplified through the use of sta-
tistical CORE (COrrelation and REgression analysis) programs
devised by Michigan State University's computer personnel.
Computer output included regression coefficients, correlation
coefficients, coefficients of determination, standard errors
of estimates, means, and standard deviations. A discussion
of these statistics will follow.

A statistical test of significance was run for each
graph using the 'f' statistic. All relationships proved
significant at the one percent level.

Simple regressions relate one dependent variable to
the independent variable. If two related (associated) series

are plotted graphically with one variable placed on the X axis
59

60
and the other on the Y axis, the result is known as the scatter
diagram. If there is a high degree of association, the scatter
will be confined to a narrow "path". The less perfect the
relationship between the two sets of data, the greater will be
the departures from the indicated line of course. The equation
for this line is mathematically determined by the least squares
technique where the sum of squares of the Y deviations of points
about the line is minimized. This regression line always passes
through the intersection of the means of X and Y (the centroid
of the data). The regression line of Y on X is of the following
form:

Y = A J-ByxX
where A is the Y intercept and Byx is the slope. The sequence
of subscript, yx, indicates a regression of Y on X or estab~
lished Y as the dependent variable.

Whether or not a correlation between Y and X exists is

indicated by the slope, B (called the regression coefficient).

yx
If the line of regression is parallel to the X axis (Byx = 0),
any value of X would predict the general mean of Y and no
correlation would exist. Furthermore, if the line is not
horizontal, the best estimate of Y would depend upon X and a
correlation would exist.

The degree of dispersion of scatter must also be estabw
lished. The standard error of estimate (S) measures the degree
of association between actual Y and estimated Y (Y value
calculated from the regression equation). The larger the

standard error of estimate, the greater the scatter about the

regression line. The standard error of estimate is in Y units.

61

The standard error of estimate can be compared with the
standard deviation. Whereas the standard deviation is the
average (quadratic mean) or the deviations about the
arithmetic mean, the standard error of estimate is the average
(quadratic mean) of the deviations about the line of regression.
Also, the standard error of estimate may be used in the same
manner as the standard deviation. Plus or minus one standard
deviation about the arithmetic mean includes 68 percent of the
cases; and plus or minus one standard error of estimate will
include 68 percent of the cases when measured about the line
of regression. (It is assumed that there is a normal or
approximately normal distribution of the values about the line
of regression). (4)

Another measure of the degree of association is the

correlation coefficient (R). R is determined by the equation:

82
B.J.-aye

where S is the standard error of estimate andcfy is the

y
standard deviation of the Y values. R is used as a means

of comparing the relative correlation of two variables to
the correlation of another pair of variables. A perfect
correlation results when R = 1.00 and no correlation results
when R = 0.00. A negative R results when an increase in one
variable causes a decrease in the other variable.

The coefficient of determination (R2) multiplied by

100 percent indicates the percent variance in Y associated

with the variance in X.

APPENDIX II

Equations

Major Tests

Because the load applied by the testing apparatus
approximated but did not equal a uniform load, it was
necessary to derive equations for MOE and MOR using the
shear and bending moment diagrams shown in Figure 28.

In determining the equation for MOE, the area
moment was used.

Statement of area moment:

 

If A and B are points on a deflection curve, the

vertical distance of B from the tangent drawn to

the curve at A is equal to the moment with respect

to the vertical through B of the area of the bending

moment diagram between A and B, divided by the

flexural rigidity EI.

In reference to Figure 28, the sum of the areas of the
squares times their centroidal distances from “A" equals
310,144P. The sum of the triangles times their centroidal

distance from “A" equals 20.768P.

[3 a 310.1uuP-k2o.268P _ 2 u w

w
EI X 13P “ EI

62

63

In the above equation, W a total load in pounds, A:
deflection in inches at center, and I - calculated moment
of inertia of the board.

In determining the equation for MOR, the flexure
formula was used:
{h
(7’: ¥Q = 222I3I 2
In the above formula, the bending moment was determined by
the area under the shear diagram to the left of the maximum

or center (222P or 222 - LL'). The 'C' was the distance to

13

the extreme fibers (g) and 'I' was the calculated moment of

inertia.

Mino£:Tests
In the minor tests, the clear wood samples were tested

using a single point load over a 14 inch span.

 

 

 

 

 

 

Free Body: 0” P
l’ ‘ 1
p “1” TP
2 1/2
The MOE was calculated using the formula:
E 3 PL3 , E = P . 2 44
EB“? ' . .1 I

where 'P' equals load, 'L' equals Span in inches (14"),
[Sequels deflection (always 0.1"), and ‘1' equals calculated
moment of inertia.

The flexure formula was used to determine MOR.

 

mg . P L[4 - h/2 . _ 21F
S = I ' S = bh5/12 ' S ‘ BE?

FREE BODY

p
f— I 20’ 7 an 8n 8“ ‘ 8" 8n 8" 7 8n 8" 8n 7 8n 8» 8n ' 2n
6'5 P 6.5 P

P P

SHEAR DIAGRAM

 

55F

 
 
 
  
  

 

.. s»
u
-u '0

b
b

78?

_—-—-—

 

 

BENNNG MOMENT
NAGRAM

 

 

78F

 

 

 

 

 

 

 

 

 

MAJOR TEST SHEAR AND BENDING MOMENT DIAGRAMS

HGURE 28

65
In the above formula '8‘ is equal to the extreme fiber stress
or modulus of rupture, SM" is the maximum moment (equal to
maximum load 'P', times L/4), 'C" is the distance from neutral
axis to extreme fiber stress (height, 'h' divided by 2) and
'I‘ is the calculated moment of inertia for the sample (%%2).
Moisture contents were determined using the oven dry

method and specific gravity was determined using the oven dry

weight and the oven dry volume.

APPENDIX III
Data

66

MAJOR TESTS MINOR TESTS

Modulus of Elasticity . Clear HOE Clear MOR .Sp. Gr.

Board EMSR Visual Mod. of
Number Grade Grade Face Back Top Bottom Rupture Average Thickness Height

 

 

 

 

 

 

 

 

 

 

 

[464 2100 UTIL 1.367 1.4 7 1 295 1.138 4617 1.409 1.286 11532 10385 . 7 1.600 7.523 1
;¥65 2100 1500 1.541 1.681 1 502 1.502 5116 1.581 1.533 12807 13"05 .54 1.505 7.116 1
L 66 2100 1200 1.510 1.456 1 360 1.226 5157 1.317 1.198 110397 10614 .46 1.609 7.504
L467 2100 IND-DATA 1.591 1.538 1 471 1.425 5887 1.283 1.290 11114 12012 .40 1.598 7.385
L468 2100 1900 1.570 1.570 1 399 1.631 7515 1.453 1.568 12419 12119 .53 1.600 7.401:5
:lp9 2100 1500 1.729 1.692 1.383 1.383 5874 1.248 1.373 10902 10526 .45 1.578 7.44944
L 70 2100 1500 1.319 1.353 1.051 1.051 2040 899 1.214 9295 79'65 .40 1.607 7.501
7 71 2100 1500 1.707 1.690 1.462 1.484 5763 1 545 1.509 11877 11655 .47 1.602 7.434:1
.6-: - 1.508 #

    

.1

 

, (:0:

MAJOR TESTS MINOR TESTS

Modulus of Elasticity Clear MOE Clear MOR Sp. Gr.

Board EMSR Visual Mod. of
Number Grade Grade Face Back Top Bottom Rupture Average Thickness Height

J ()3

 

 

 

 

 

 

 

 

. . e a e ‘ . ’ e h u - u I . . J
L; 97 2100 1200 1.480 1.462 1.148 1.235 4717 1.349 1.400 10987 11585 .43 1.592 7303144
1 98 2100 1200 1.897 1.841 1.534 1.552 4949 1.545 1.653 13663 12290 .47 1.563 7.4‘3_J
L; 99 2100 1200 1.404 1.404 1.256 1.169 3208 1.3387 1.262 11088 10563 .46 1.587 7.50:::
:;100 2400 2050 1.813 1.968 1.762 1.985 6916 1.500 1.618 13362 14181 .51 1 603 7.48444
L.101 2400 1900 1.701 1.701 1.528 1.551 4734 1.181 1.331 10826 12495 .46 1 607 7.467 1
:j102 2100 1500 2.113 2.113 1.592 1.664 7413 1.701 1.587 13438 11988 .42 1 588 7.358 T
1* 103 2400 1500 1.670 1 1.430 1.496 8728 1.369 1 l 620 7.499 1

.321 10951 10909 .40

-

   
  

s e-

‘ . e- o.

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

i:109 2400 1200 1.658 1.641 1.631 1.595 4321 1.632 1.568 11261 12462 .45 1.597 7.412 :
L,110 2400 1500 1.614 1.614 1.626 1.564 6222 1.433 1.612 11737 13671 .49 1.593 7.513 J
L_111 2400 MISS. 2. 57 2.057 1.683 1t659 8882 2.166 1.788 13196 13658 .49 1.600 7.151 J
1 112 2400 1200 1.72- 1.706 1.435 1.457 7129 1.193 1.221 10373 10962 .45 1.605 7.475g4
L_113 2400 1500 2.152 2.135 1.832 1.786 6745 1.457 1.587 12331 13371 .48 1.608 7.491 1
L 114 2400 UTIL 1.952 1.952 1.545 4T1.639 11062 1.604 112427 12634 12341 .48 1.590 77.392 1
115 2400 1200 1.959 1.941 1.591 1.649 5065 1.667 1.577 12731 12733 .51 1.589 7.150 1
. 116 2400 1200 2.026 1.957 1.885 1.885 1072 1.693 1.3947 13296 12187 .51 1.603 7 64)::
L 1177 2400 1500 1.891 1.838 1.720 1.838 5464 1.77” 1.622 13507 14021 .49 1.588 7.150
L 118 2400 2050 2.094 2.203 1.834 1.859 116‘5 1.758 1.720 14487 13929 .53 1.590 7.‘7’ ;
L_119 2400 1900 1.888 1.888 1.696 1.662 10383 1.606 1.598 12498 12558 .46 1.600 7.500
##1207 2400 1200 21116 2.298 1.736 1.711 7468 1.670 1.773 12558 13177 .51 1.582 7.368
F 121 2400 1500 1.869 1.902 1.572 1.394 8763 1.511 1.343 12255 11690 .51 1.632 7.4667fi
L*122 2400 1500 2.139 2.104 1.883 1.930 10429 1.679 1.645 12663 13196 .47 1.610 7.452 #
;7123 2400 1900 1.916 1.898 1.634 1.704 9550 1.454 1.169 14063 7954 .54 1.595 7 uji:]
9‘124 2400 1200 2.003 2.021 1 727 1.656 3951 1.791 1.491 13583 11325 .51 1.590 7 4034;
125 2400 1500 1.657 1.75 1.202 1.245 5602 1.452 1.155 12465 10416 .45 1.608 7.196

-

.

 

 

 

 

 

- . . . . . . 2 . .. . - .(U .
fi146 2400 1500 2.408 2.302 2.031 2.114 11436 1.765 1.866 13889 14375 .50 1 597 7 377 j
I 147 2400 1200 1.858 1.949 1.595 1.75 9503 1.612 1.580 13955 13885 .52 1 634 7.112 3
{:148 2400 1200 1.397 1.397 1.205 1.276 2445 1.309 1 358 10521 10635 .43 1.605 7.440_::
[ 149 2400 2050 1.900 1.937 1.976 1.989 11770 1.783 1.727 14695 14247 .50 1 ’75 7 s86::
I 150 2400 1200 1.919 1.971 1.580 1.557 8348 1.413 1.503 11364 12123 .47 1.593 7 I79 1

 

10.

11.

12.

13.

LITERATURE CITED

Anon., "A Positive Stress Grader", Lumberman 88(10), 1961.

Anon., "Two Stress Grading Machines in Action", Forest
Industries 90(9), 1963.

Anon., "Fully Automatic Stress-Grading Machines", Timber
Trades Journal 246(4536), 1963.

Arkin, H. and Colton R.R., An Outline of Statistical
Methods, 4th ed., New York, Barnes and Noble, 1950.

Forest Products Laboratory, Wood Handbook, U.S. Department
of Agriculture Handbook No. 72, 1955.

Hoyle, R.J" "A Non-Destructive Test for Stiffness of
Structural Lumber", Forest Products Journal 11(6),
1961.

. Hoyle, B.J., "Annual Review in Wood Engineering", Forest

Products Journal 14(9), 1964.

Kramer, P.R., "Correlation of Bending Strength and Stiffness
of Southern Pine", Forest Products Journal 14(10), 1964.

Senft, J.F., Suddarth, S.K. and Angleton, H.D., "A New
Approach to Stress Grading of Lumber", Forest Products
Journal 12(4), 1962.

Sunley, J.G. and Curry, W.T., "A Machine to Stress Grade
Timber", Timber Trades Journal 241(4472).

Sunley, J.G. and Hudson, W.M., "A Report of Research on
the Machine Grading of Lumber in Britain", Forest
Products Journal 14(4), 1964.

Wood, L.W., "Machine Graded Lumber, Out of the Laboratoryn-

Into Commercial Trials", Forest Products JQurnal 14(1),
1964.

Wood, L.W. and Soltis, L.A., "Stiffness and Shrinkage of
Green and Dry Joists", U.S. Forest Products Research
Note. Forest Products Laboratory, Madison, Wisconsin,
FPL 15.

69

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